Question

$x^2y - 2xy - 24y = y(x^2 - 2x - 24)$
what is the completely factored form of
$x^2y - 2xy - 24y$
$(xy + 4)(x - 6)$
$xy(x + 4)(x - 6)$
$y(x + 4)(x - 6)$
$y(x + 4)(xy - 6)$
done

Explanation:

Step1: Factor out GCF

$x^2y - 2xy - 24y = y(x^2 - 2x - 24)$

Step2: Factor quadratic trinomial

Find two numbers: $4$ and $-6$, since $4+(-6)=-2$ and $4\times(-6)=-24$.
$x^2 - 2x - 24 = (x+4)(x-6)$

Step3: Combine factors

Substitute factored trinomial back: $y(x+4)(x-6)$

Answer:

$\boldsymbol{y(x + 4)(x - 6)}$ (Option 3)